How would you fill this shape

I would use the shape builder tool.

Here is how it works. I use it all of the time in these scenarios.

https://www.lauracoylecreative.com/illustrator-tips/shape-builder-tool-workflow

or a more basic approach to learning the tool is below;

https://helpx.adobe.com/illustrator/using/creating-shapes-shape-builder-tool.html

The trick needs to be done with two copies of the same head shape positioned on top of each other. One copy of the head would only have a fill and no line stroke. That shape has to be solid with no line work extending inside of the path. That will allow the fill to be solid. The other copy of the head would have a line stroke but no fill. Use that copy to have the part of the ear going inside the head shape. Obviously that object would be stacked on top of the other copy of the head shape.

I would try Live Paint:

https://helpx.adobe.com/illustrator/using/live-paint-groups.html